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Laser Physics

Level mixing induced transparency

R. N. Shakhmuratov, J. Odeurs, S. Gheysen, Yuri V. Rostovtsev, Olga A. Kocharovskaya, Paul Mandel

Published May 1, 2007• 0 citations
Publisher

Abstract

We discuss level mixing induced transparency (LMIT), which is experimentally found in a thick absorber of FeCO3 containing the 57Fe Mössbauer nuclei. LMIT is observed if two hyperfine levels of the excited state nucleus cross. Absorption of gamma radiation drops by about 25% with respect to the sum of two overlapping absorption lines. The absorption deficit is explained by the mixing of the crossing levels with a symmetry breaking interaction. The level mixing induces a polarization change of the scattered radiation. In such a way, the radiation develops in “normal modes,” which are less absorbed in a thick absorber. We show that, in spite of the absorption drop, the area of the absorption line does not change. This confirms the general knowledge that interference phenomena (destructive or constructive) do not change the lifetime of an excited state particle (atom, nucleus, etc).

DOI
10.1134/s1054660x07050180

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We discuss level mixing induced transparency (LMIT), which is experimentally found in a thick absorber of FeCO3 containing the 57Fe Mössbauer nuclei. LMIT is observed if two hyperfine levels of the excited state nucleus cross. Absorption of gamma radiation drops by about 25% with respect to the sum of two overlapping absorption lines. The absorption deficit is explained by the mixing of the crossing levels with a symmetry breaking interaction. The level mixing induces a polarization change of the scattered radiation. In such a way, the radiation develops in “normal modes,” which are less absorbed in a thick absorber. We show that, in spite of the absorption drop, the area of the absorption line does not change. This confirms the general knowledge that interference phenomena (destructive or constructive) do not change the lifetime of an excited state particle (atom, nucleus, etc).
We present a detailed description and a consistent explanation of the transparency observed in the Mössbauer absorption spectra at a nuclear level mixing in FeCO3. We develop a model for scattering in this nuclear Λ system in a Maxwell–Schrödinger approach, taking into account multiple scattering and polarization effects. It is shown that the level mixing scheme not only yields an expected Stark splitting, but, due to the unequal relaxation rates and transition strengths, an additional interference term is present. Therefore, this scheme is equivalent to the Λ scheme considered for EIT in quantum optics. The interference in the absorption of the gamma radiation can be destructive, leading to a partial transparency, but can also be constructive. Both types of interference are present in the observed spectra.
We present a fully quantum mechanical treatment of resonant scattering of gamma radiation in a nuclear Λ-scheme. Simulations of the closed-form solution for the radiation intensity for N effective scatterers contributions are compared with Mössbauer spectra of FeCO3. It is shown that, although the nuclear level mixing scheme does not fulfill EIT conditions, the observable effects are similar. The change in polarization of the scattered radiation, due to level mixing, gives rise to the development of a strong complementary polarization state which is delayed with respect to the incident photon and to a reduction in absorption because this state does not interfere with the incident photon.
We have observed the effect of electromagnetically induced transparency (EIT) in a nuclear system. A series of Mössbauer measurements was performed on a single crystal of natural FeCO3. When the condition of nuclear level crossing is fulfilled, a clear reduction in absorption or transparency is seen at the point of level crossing. This reduced absorption cannot be ascribed to saturation effects because of the specific geometry of the experiment. We present an explanation in terms of level mixing by a small non-axial component of the electric field gradient. It can be shown that such a scheme is equivalent, at least in principle, with the schemes considered for EIT in quantum optics.
The so-called gamma-echo effect has been observed experimentally and analyzed using the semiclassical optical theory. Here the effect is reinterpreted using a new 1D quantum mechanical model. This leads to a different interpretation of the effect as a π phase-shift induced transparency. In the basic time-differential Mössbauer spectroscopic technique the forward-scattered recoil-free radiation is observed, in delayed coincidence, after passing through a nuclear-resonant absorber. The effect in question is produced most efficiently when the source of recoil-free radiation is moved abruptly causing a π phase shift of the source radiation during its radiative lifetime. Using the 1D model the effect is seen to arise from the constructive interference between the source radiation at a later time, and the radiation coming from the absorber excited at an earlier time. The exact form of the source modulation and the nuclear-resonant thickness of the resonant absorber determines the shape of the time-differential resonant gamma ray transmission spectrum. Numerical results are given using the familiar 57Fe recoil-free resonant transition. The π phase-shift-induced transparency allows the resonant gamma radiation, incident on the resonant absorber, to be transmitted through the absorber without appreciable attenuation.
Due to the virtual photon exchange between atomic nuclei and the field of zero-point electromagnetic oscillations, some nuclei of a given sample are in a virtual excited state with the lifetime ∼ħ/ E , where E is the energy of nuclear level. For 57 Fe nuclei, whose first excited state has an energy of 14.4 keV, this time is equal to ∼4.6×10 −20 s. If a thin 57 Fe Mössbauer gamma-ray absorber is surrounded by a thick screen of the same atoms, the number of virtual excited nuclei in the absorber decreases and, at first glance, it should more strongly absorb Mössbauer gamma rays emitted by an external source and passing through the absorber. In this work, the ratio of the intensities of 14.4-keV gamma rays emitted by the 57 Fe nuclide and passing through the thin resonant absorber is measured in the absence and presence of the resonant screen around the absorber. Comparison shows that these ratios measured for the gamma source at rest and in the oscillating state differ by 0.00123±0.00075. This value should be treated as the upper limit for the desired effect under these experimental conditions.